KABUL, Afghanistan (AP) -- Taliban insurgents fired rocket-propelled grenades, heavy machine guns and assault rifles at the U.S. Embassy, NATO headquarters and other buildings in the heart of the capital Tuesday while suicide bombers struck police buildings in an attack blitz that displayed the ability of militants to bring their fight to the doorsteps of Western power in Afghanistan.

The coordinated assaults - coming two days after the United States marked the 10th anniversary of the Sept. 11 terror attacks - carried an unsettling message to Western leaders and their Afghan allies about the resilience and reach of the Taliban network.

It was the third major attack in Kabul since late June, casting fresh doubts on the ability of Afghans to secure their own country as the U.S. and other foreign troops prepare to withdraw by the end of 2014.

The American Embassy and NATO both said no staff were wounded. Afghan officials said the violence around Kabul resulted in the deaths of four police officers and two civilians. Another 12 people were wounded, including at least four caught up in suicide bombings in the western part of the capital.

Four Afghans were wounded when a rocket-propelled grenade hit the original U.S. embassy building next to the new embassy, CIA Director David Petraeus told lawmakers on Capitol Hill. Among them was a small girl who was with a group waiting for visas outside the embassy, he said.

The surge of violence was a stark reminder of the instability that continues to plague Afghanistan nearly a decade after the U.S. invasion that ousted the Taliban for harboring al-Qaida, which carried out the 9/11 plane hijackings.

In Washington, Secretary of State Hillary Rodham Clinton said the U.S. will do everything it can to combat those who committed the "cowardly attack."

Clinton said the U.S. was moving to secure the area and "ensure that those who perpetrated this attack are dealt with." She said the U.S. would assist Afghans injured in the attack.

In Brussels, NATO Secretary-General Anders Fogh Rasmussen said the "enemies of Afghanistan" were trying to disrupt the handing over of security responsibility to the Afghan army and police.

President Hamid Karzai condemned the attack and said that it would not deter Afghan security forces from taking full responsibility for the country's security by the time the international community withdraws all its combat troops at the end of 2014.

"By carrying out such attacks terrorists cannot stop the transition of security from international to Afghan forces," Karzai said in a statement.

Gunfire and explosions resounded across Kabul well into the afternoon. At least two insurgents were still on the top floors of a nine-story building by late evening, police said.

Earlier, plumes of smoke rose from the area near the embassy, and U.S. Army helicopters buzzed overhead. The American Embassy is on the edge of the Wazir Akbar Khan area, which is home to a number of other foreign missions.

Gunmen fired from the nine-story office building that is under construction at Abdul Haq square, which is about 300 yards (meters) from the U.S. Embassy. Afghan official said the attack began when about half a dozen insurgents took over the building and began firing toward the embassy and the adjacent NATO headquarters.

Thee military coalition, also known as ISAF, said the insurgents were firing rocket propelled grenades and small arms.

"An Afghan-led response is under way against the attack near the U.S. Embassy and ISAF HQ," NATO said in a statement.

As part of the attempt to secure the building, an Afghan army MI-35 attack helicopter opened fire on the top floors with its heavy 12.7 mm gatling gun.

Explosions in areas located nearly a mile (kilometer) from the building indicated that the insurgents had heavy weaponry. Taliban spokesman Zabiullah Mujahid claimed the Taliban fighters were equipped with a 82 mm mortar, heavy machine guns, rocket propelled grenades, AK-47 assault rifles and that all were wearing suicide vests.

Abdul Jabbar, a bus driver who witnessed the beginning of the attack, said at least one insurgent was firing from the roof and that they "had heavy machine guns, heavy weapons like rockets and RPG's and AK-47's."

The Kabul police said at least seven insurgents were involved in the attacks around the city. Four were involved in the attack from the building and three attempted to carry out suicide attacks.

All three suicide attackers were killed by police: one on the road leading from the capital to the airport, and two when they tried to attack Afghan police buildings in western Kabul, across the city from the site of the embassy attack. One was shot by police; the bullets detonated his vest and injured two police officers. The other one detonated his vest at a nearby building, wounding two civilians.

U.S. Embassy spokeswoman Kerri Hannan said that staff had been ordered to take cover in hardened structures.

"We can confirm there are no casualties at this time among embassy personnel," she said.

NATO also said none of its staff were wounded in the attack. It said the U.S.-led coalition was providing air support to Afghan security forces.

At least one rocket landed on a building housing privately owned Tolo TV and another near a minivan carrying school children.

Associated Press reporters saw police carrying the body of a civilian man, dressed in a white tunic and pants. He was hit by a rocket that landed in the Wazir Akbar Khan neighborhood, police said. A cameraman from Iran's Press TV was wounded by an explosion near their offices in the same neighborhood.

Mujahid said the attacks were proof that the Taliban "are strong and whatever false claims the Afghan government or the invading forces say about the mujahedeen being weak is not true. These attacks show the strength of the mujahedeen."

Violence in the once-quiet capital has escalated in recent months.

On Aug. 18 Taliban suicide bombers stormed a British compound in an upscale Kabul neighborhood, killing eight people during an eight-hour firefight as two English language teachers and their bodyguard hid in a locked panic room. Those killed included five policemen, a municipal worker, a security and a New Zealand special forces soldier who was shot in the chest as he tried to free the hostages - who survived.

On June 29, nine insurgents wearing suicide vests stormed the Intercontinental Hotel armed with rifles and rocket launchers on the eve of a major conference on Afghan governance. They killed at least 12 people and held off NATO and Afghan forces for five hours, until U.S.-launched helicopter airstrikes killed the last insurgents hiding on the roof.

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Associated Press writers Patrick Quinn and Heidi Vogt contributed to this report.

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